According to Shaw, Professor Higgins has "touches of sweet". Bring out the pathos in Higgins' character in light of Shaw's observation.

This question misunderstands Shaw's quote in the preface to Pygmalion. When Shaw mentions "touches" of Sweet in the play, he means Henry Sweet, a renowned phonetician and grammarian who studied accents and pronunciation, just as Higgins does. What Shaw writes is the following:

With Higgins's physique and temperament Sweet might have set the Thames on fire.

When Shaw adds that there are "touches of Sweet " in the play, he is not referring to "sweet"...

This question misunderstands Shaw's quote in the preface to Pygmalion. When Shaw mentions "touches" of Sweet in the play, he means Henry Sweet, a renowned phonetician and grammarian who studied accents and pronunciation, just as Higgins does. What Shaw writes is the following:

With Higgins's physique and temperament Sweet might have set the Thames on fire.

When Shaw adds that there are "touches of Sweet " in the play, he is not referring to "sweet" aspects in Henry Higgins' personality. According to Shaw's preface, Henry Sweet was anything but "sweet," having a "Satanic contempt" for people who disagreed with his views.

Nevertheless, the question asks us to explore whether Higgins has a "sweet" side or "pathos" to his character. Higgins is rude from beginning to end, but his pathos is that he is rude without any intention of being spiteful or malicious. He is rude simply because he speaks his mind bluntly. There is a pathos in his blindness to how much he bullies Eliza and the extent to which he treats people as objects to be used rather than as human beings. His pathos may lie in how often he lacks self-awareness of the ways in which he offends people. 

For despite all his rudeness and bullying, Higgins also has moments of insight that add pathos to his character. When he and Eliza are quarreling and she says she wants to be independent, he says:

"We are all dependent on one another, every soul of us on earth."

A few moments later, he acknowledges his appreciation of her, revealing that he can have some awareness of others:

"Five minutes ago you
were like a millstone round my neck. Now you're a tower of strength: a consort battleship. You and I and Pickering will be three old bachelors together instead of only two men and a silly girl."

We feel sympathy for Higgins because he is trying to be kind but doesn't understand that Eliza has no desire to be an "old bachelor" like him.